Bernard Bolzano

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Bernard Bolzano, lithograph by Josef Kriehuber , 1849 after Heinrich Hollpein

Bernardus Placidus Johann Nepomuk Bolzano (born October 5, 1781 in Prague ; † December 18, 1848 there ) was a Catholic priest , philosopher and mathematician . The Bolzano-Weierstrass Theorem is named after him.


Bolzano's father was an art dealer from Nesso ( Como Province , Italy), his mother the daughter of a German merchant from Prague. His younger brother was the Prague physician Peter Bolzano (1794-1818). In his childhood he was strongly influenced by the religiosity of his family. Even in his youth he occupied himself with scientific and political literature.

After attending grammar school from 1791 to 1796, he studied philosophy, mathematics and physics at Charles University in Prague . In the fall of 1801 he began to study theology, and then in the winter semester 1804/05 he became Dr. phil. PhD. From 1786 to 1872, only an examination and no dissertation was required at Austrian universities. In 1805 he was ordained a priest and provisional holder of the newly established chair for the philosophy of religion . Although he also tried to get the chair for elementary mathematics , this was filled elsewhere. On October 2, 1806, he was appointed full professor.

He became a member of the Royal Bohemian Society of Sciences on February 19, 1815 and in 1818 dean of the Philosophical Faculty of Prague University and director of the natural science department of the Royal Bohemian Society of Sciences.

He was admired by his students for his liberal and bohemian-patriotic views. Bolzano, son of an Italian and a German from Prague, wanted to overcome nationalisms in an overarching Bohemian patriotism. Josef Mühlberger writes in his History of German Literature in Bohemia (Munich-Vienna 1981): “He also counted nationalism among the dividing barriers. Bolzano became a founder and a pillar of bohemism, who, beyond the two nations of the country, felt obliged to the Bohemian land common to both nations with equal love and responsibility. ”His lectures were characterized by social criticism and analytical acumen. Bolzano criticized the Austrian constitution and represented pacifist and socialist views, which is why he was removed from office by Emperor Franz I on December 24, 1819, based on alleged heresy . He was forbidden to continue taking on public activities. His release was the culmination of an investigation against Bolzano that lasted from 1816 to 1825, in which he was threatened with imprisonment. The first volume of his edification speeches (1813) and his textbook on religious studies were placed on the index in 1828 and 1839, respectively. After Francis I died in 1835, Bolzano's surveillance was eased and in the 1840s he was allowed to publish non-theological works in the treatises of the Royal Bohemian Society of Sciences.

Bolzano's grave in the Olšanské hřbitovy cemetery in Prague

From 1823 he spent the summer months in the South Bohemian village of Těchobuz on the estate of the Hoffmann family. From 1830 on he lived there entirely. In the 1830s, he focused his studies on real numbers . He wrote a work on real functions and found the first example of a continuous, nowhere differentiable function ( Bolzano function ).

Shortly before Anna Hoffmann died in 1842, he returned to his brother in Prague. On December 18, 1848, Bolzano also died in Prague, leaving behind an extensive handwritten legacy.

In 1885 in Prague, near today's main train station, the then newly built Bolzanova Street was named after him. The street still bears his name today. In 1975 the Bernhard-Bolzano-Gasse in Vienna- Floridsdorf was named after him. The asteroid of the main outer belt (2622) Bolzano was named after him.


As a mathematician, he carried out basic research in analysis . He was probably the first to construct a function that is continuous everywhere , but nowhere differentiable ( Bolzano function ). He also dealt with large and infinitely small numbers.

In an essay from 1817 he proved the intermediate value theorem and introduced Cauchy sequences , four years before Augustin-Louis Cauchy . In contrast to those of Cauchy, Bolzano's work on a stricter foundation of analysis was hardly noticed by his contemporaries and was only appreciated in the second half of the 19th century (for example by Hermann Hankel , Hermann Amandus Schwarz , Otto Stolz ). Bolzano-Weierstrass's mathematical theorem is named after him .

In the work "Paradoxien des Infendlichen", published posthumously in 1851, he collected a multitude of knowledge about (finite and infinite) sets and introduced the term set as a technical term in mathematics.

Bolzano's philosophical work is of great importance. In his four-volume science studies in particular, he anticipated numerous developments and tendencies in later phenomenology and later analytical philosophy. The range of his philosophical work is also remarkable: It ranges from utilitarianism ( ethics ), logic , ontology , epistemology and science theory , aesthetics to the philosophy of religion , whereby Bolzano also deals with general questions of social life in his edification speeches (e.g. love of the country).

Because of Bolzano's opposition to imperial authority, many of his works remained in manuscript form during his lifetime and were only rediscovered late after his death. Below are some of his works by year of publication.

  • 1810: Contributions to a more well-founded presentation of mathematics
  • 1810: About love of fatherland ( online )
  • 1816: The binomial theorem
  • 1816: About the relationship between the two ethnic groups in Bohemia ( online )
  • 1817: Purely analytical proof of the theorem that between two values ​​that grant an opposite result there is at least one real root of the equation
  • 1827: Athanasia or reasons for the immortality of the soul
  • 1834: Textbook of religious studies
  • 1837: Science
  • 1843: On the concept of the beautiful
  • 1849: On the division of the fine arts
  • 1851: Paradoxes of the Infinite ( online )
  • 1867: Anti-Euclid
  • 1875: size theory


Critical work edition

  • Bernard Bolzano: Complete Edition, 132 vols. , Ed. by Eduard Winter , Jan Berg, Friedrich Kambartel, Jaromír Loužil, Edgar Morscher and Bob van Rootselaar. Frommann-Holzboog, Stuttgart-Bad Cannstatt 1969 ff., ISBN 978-3-7728-0074-0 .

Further primary literature

Secondary literature

  • Kurt Blaukopf: The Aesthetics of Bernard Bolzano. Conceptual criticism, objectivism, “real” speculation and approaches to empiricism . Sankt Augustin 1996.
  • Curt Christian: Bernard Bolzano, life and effect . Vienna 1981.
  • Peter Demetz : Bernard Bolzano - Language Theory and Nationality Conflict . in id. Bohemian Bohemia , Vienna 2006.
  • Peter Demetz : In the footsteps of Bernard Bolzano. Essays. Arco, Wuppertal u. Vienna 2013. ISBN 978-3-938375-49-5 .
  • Vojtech Jarnik: Bolzano and the Foundations of Mathematical Analysis . Prague 1981.
  • Edgar Moscher: Bernard Bolzano's intellectual legacy for the 21st century . Vienna 1999.
  • Lubos Novy, chapter Bolzano, in Hans Wussing , W. Arnold: Biographies of important mathematicians . Berlin 1983.
  • Steve Russ: The Mathematical Works of Bernard Bolzano . Oxford University Press, Oxford, 2004.
  • Giuseppe Rutto: Bernard Bolzano. Reform Catholicism e utopia nella Praga della restaurazione . 1984.
  • Jan Sebestik: Logique et mathématique chez Bernard Bolzano . Librairie Philosophique J. Vrin, Paris, 1992.
  • Otto Stolz: B. Bolzano's importance in the history of calculus . Mathematische Annalen Vol. 18, 1881.
  • Kurt Strasser: Bernard Bolzano (1781–1848): a Bohemian enlightener , Vienna; Cologne; Weimar: Böhlau Verlag, [2020], ISBN 978-3-412-51750-2
  • Achim Vesper: Observing and distinguishing. Bolzano on the concept of aesthetic perception . in: A. Bauereisen / S. Pabst / A. Vespers (ed.), Art and Knowledge. Relationships between aesthetics and epistemology in the 18th and 19th centuries . Würzburg 2009, pp. 103-118.
  • Karl Werner:  Bolzano, Bernhard . In: Allgemeine Deutsche Biographie (ADB). Volume 3, Duncker & Humblot, Leipzig 1876, pp. 116-118.
  • Klaus-Gunther Wesseling:  BOLZANO, Bern [h] ard (baptismal name: Bernardus Placidus Johann Nepomuk B.). In: Biographisch-Bibliographisches Kirchenlexikon (BBKL). Volume 16, Bautz, Herzberg 1999, ISBN 3-88309-079-4 , Sp. 152-199.
  • Eduard Winter:  Bolzano, Bernard. In: New German Biography (NDB). Volume 2, Duncker & Humblot, Berlin 1955, ISBN 3-428-00183-4 , pp. 438-440 ( digitized version ).
  • Eduard Winter: Bernard Bolzano. A picture of life . Stuttgart 1969.
  • Constantin von Wurzbach : Bolzano, Bernhard . In: Biographisches Lexikon des Kaiserthums Oesterreich . 2nd part. Publishing house of the typographic-literary-artistic establishment (L. C. Zamarski, C. Dittmarsch & Comp.), Vienna 1857, pp. 35–39 ( digitized version ).
  • Gregor Zeithammer: Bolzano, biography (1836) . Stuttgart 1997.

Web links

Wikisource: Bernard Bolzano  - Sources and full texts
Commons : Bernard Bolzano  - Collection of images, videos and audio files

Individual evidence

  1. ^ Lutz D. Schmadel : Dictionary of Minor Planet Names . Fifth Revised and Enlarged Edition. Ed .: Lutz D. Schmadel. 5th edition. Springer Verlag , Berlin , Heidelberg 2003, ISBN 978-3-540-29925-7 , pp.  186 (English, 992 pp., [ONLINE; accessed on August 28, 2019] Original title: Dictionary of Minor Planet Names . First edition: Springer Verlag, Berlin, Heidelberg 1992): “1981 CM. Discovered 1981 Feb. 9 by L. Brožek at Kleť. ”
  2. Ivor Grattan-Guinness suspected an influence of Bolzano on Cauchy in Bolzano, Cauchy and the new analysis in the early 19th century (Archive for the history of exact sciences, Vol. 6, 1969/1970, pp. 372-400), But what was contested by Hans Freudenthal , among others : Did Cauchy plagiarize Bolzano? . Archive Hist. Exact Sciences Vol. 7, 1971, p. 375.